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Life and death
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==Status of a group== The concept of 'status' is discussed in ''Life and Death'' by James Davies. Groups of stones are divided into those that are ''alive'', ''dead'' or ''unsettled''. Here ''alive'', for example, is an unconditional judgement made, that with best play from both players, the group can survive to the end of the game. That assumes the ''opponent'' starts: the alive status means that, whatever the attack made, there is an adequate defensive answer. The ''unsettled'' status is therefore most worthy of attention. By playing first, the attacking player can kill such a group. By playing first, the defending player can save such a group. There is an enormous range of formations that are unsettled. A group can be considered "alive", "dead", or "unsettled" based on whether two eyes can be made regardless of how the opponent plays. Naturally, one space is insufficient. Two adjacent spaces are insufficient to make two eyes as well, since putting a stone in will create one eye only. The opponent can simply fill in one of the two spots, threatening to fill in the other, forcing the player to capture that one by playing in the second one. Then, the opponent simply plays there again, killing the group. Usually this will not be done during the game, but at the end, during calculation, the group will be labeled "dead" and removed as prisoners. The only way to actually remove a group from the board is to fill its "eye space" with all but one, forcing it to capture the filling-in group by putting a stone in the last space. If the created group is not alive, then continuing this process will eventually kill the entire group. ===Status of groups of three=== <div class="thumb tright"> <div class="thumbinner" style="width:184px; font-size: 100%;"> {{Goban 9x9 | ul| b| w| u| u| w| b| u|urc | lc| b| w| | | w| b| b| r | l| b| w| | | w| w| b| b | b| b| w| | | | w| w| w | w| w| w| | | | | | r | l| | | | | | | | r | l| | | | | | | | r | l| | | | | | | | r | dl| d| d| d| d| d| d| d| dr|20}} <div class="thumbcaption" style="font-size: 88%;"> Unsettled groups with three empty points </div> </div> </div> There are two possible groups of three, an "r" [[Shape (Go)|shape]] and three in a line. Both of these are unsettled, as whoever plays obtains the desirable result. The person trying to create two eyes can play in the middle spot (the one connected to the other two) and the other two are now eyes. If the opponent plays, they will play in the same spot, followed by an adjacent spot (the other player's piece would be captured were they to play in one of the two open spots), leaving only one empty spot left. This forces the first player to capture, leaving the dead two shape. The critical points are circled in the "Unsettled groups with three empty points" diagram. ===Status of groups of four=== <div class="thumb tleft"> <div class="thumbinner" style="width:224px; font-size: 100%;"> {{Goban 11x11 | ul| uc| uc| u| b| w| b| b| b| b| w | b| b| b| b| b| w| b| | c| b| w | w| w| w| w| w| w| b| b| c| b| w | b| b| b| w| | w| w| b| | b| w | l| c| b| b| w| | w| b| b| b| w | b| c| | b| w| | w| w| w| w| w | b| b| b| b| w| | | | | | r | w| w| w| w| w| w| w| w| w| w| w | w| b| b| b| w| w| b| b| b| b| w | b| b| | b| b| w| b| | | b| w | b| d| dc| d| b| w| b| d| d| b| w|20}} <div class="thumbcaption" style="font-size: 88%;"> Groups with four empty points </div> </div> </div> With four blank spots, there are [[tetromino|five unique shapes]]. Three are alive, one is unsettled, and one is dead. The three alive ones are the straight line, L and Z shape. If the opponent plays in any spot, the first player can live by playing in the adjacent spot in the center two. In the diagram "Groups with four empty points" black's groups in the upper corners are alive. If the opponent plays any of the circled positions, playing the other circled position will secure the status of the black group. The unsettled shape is the four-stone pyramid, shown in the left bottom corner. Whoever plays in the circled center spot gets the desired result, so the player whose move it is wins. A two-by-two square space is dead: if black plays in the top left corner of the two-by-two square, white can respond by playing in the bottom right corner (see the L-shaped case in the previous section). On the other hand, if white wants to capture the black group, they only have to play anywhere inside the square, and there will be no way for black to avoid capture. ===Status of groups with more than four empty points=== There are no dead shapes with more than four empty points, though there are a couple of unsettled ones. <div class="thumb tright"> <div class="thumbinner" style="width:184px; font-size: 100%;"> {{Goban 9x9 | b| u| uc| u| b| w| u| u| ur | b| | | b| b| w| | | r | b| b| b| b| w| w| | | r | w| w| w| w| w| | w| w| w | l| | | w| | w| b| b| b | l| | | | w| b| b| | b | l| | | | w| b| | c| r | l| | | | w| b| b| | b | dl| d| d| d| w| w| b| b| b|20}} <div class="thumbcaption" style="font-size: 88%;"> Unsettled groups with five empty points </div> </div> </div> A five stone "plus sign" (the X [[pentomino]]) and a "bulky five" (the P pentomino consisting of a square and one point off it, similar shape to a fist with the thumb extended") are the two unsettled ones. Playing in the point that touches the most others (four in the "plus sign" - center point, three in the "bulky five" - the one point in the square touching the outside point) will give the desired result to whoever does so. <div class="thumb tright"> <div class="thumbinner" style="width:184px; font-size: 100%;"> {{Goban 9x9 | b| b| b| b| w| w| u| u| ur | b| | | b| b| w| | | r | b| | c| | b| w| | | r | b| b| | b| b| w| | | r | b| b| b| b| w| | w| | r | w| w| w| w| | w| w| w| w | l| | | | w| b| b| b| b | l| | | | w| b| | c| r | dl| d| d| d| w| b| d| A| dr|20}} <div class="thumbcaption" style="font-size: 88%;"> Unsettled groups with six empty points </div> </div> </div> There are two unsettled six shapes, and the rest are all alive (see also miai). One shape is the "rabbity six" β a square, plus adding the two points touching any one of the corners. (Similar to the plus sign five, but add any of the four taken corner points to get the unsettled six.) The opponent playing in the center point threatens to fill all but one spot with a bulky five shape, and there is no defense. The other is the rectangular six ''in the corner''.<ref>[https://senseis.xmp.net/?RectangularSix rectangular six anywhere else] is alive.</ref> The opponent playing first in the top middle of the rectangle can kill the group. The defender playing first can save it by playing either there, or at the lower middle (denoted ''a''). Any group surrounding more than six points is alive, but it may be necessary to respond correctly if the opponent attacks. Additionally, because of special properties of the corner, a group with more than six points might not be unconditionally alive, as it is possible for the opponent to make an eye or two within its territory.
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